论文标题
不变差分运算符环的自动模块
Holonomic modules for rings of invariant differential operators
论文作者
论文摘要
我们研究了有限的krull维度相对于有限群体的任意行为，在具有有限的Krull维度的仿射交换域上的不变差分运算符环的全体模块。我们证明了这些环的伯恩斯坦不平等。我们的主要工具是Bavula引入的滤波器尺寸。我们扩展了Weyl代数的不变式的结果，相对于有限组的合成性作用，对于商在线性作用下不变的差分运算符对商的不变性差分运算符和某些常规Weyl代数的不变性。我们表明，上述代数的所有滤波器维度等于1。
We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals 1.
